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• Static-semantics

Get-builtin-function-in/out/pre-post

Retrieve the inputs, outputs, precondition, and postcondition of a built-in function.

Signature

(get-builtin-function-in/out/pre-post name types) 
  → 
(mv err? foundp inputs outputs precondition? postcondition?)

Arguments

name — Guard (identifierp name).

types — Guard (type-listp types).

Returns

foundp — Type (booleanp foundp).

inputs — Type (typed-variable-listp inputs).

outputs — Type (typed-variable-listp outputs).

precondition? — Type (maybe-expressionp precondition?).

postcondition? — Type (maybe-expressionp postcondition?).

This ACL2 function implicitly defines the inputs, outputs, preconditions, and postoconditions of the built-in functions. At this time, there is no other explicit representation of them in the Syntheto abstract syntax of top-level constructs.

The current built-in functions are polymorphic. The types argument of this ACL2 function specifies which monomorphic instance is being referenced.

The names of the currently supported built-in functions are in *builtin-function-names*.

Definitions and Theorems

Function: get-builtin-function-in/out/pre-post

(defun get-builtin-function-in/out/pre-post (name types)
 (declare (xargs :guard (and (identifierp name)
                             (type-listp types))))
 (let ((__function__ 'get-builtin-function-in/out/pre-post))
  (declare (ignorable __function__))
  (cond
   ((identifier-equiv name (identifier "empty"))
    (b* (((unless (= (len types) 1))
          (mv (list :builtin-wrong-types
                    (identifier-fix name)
                    (type-list-fix types))
              nil nil nil nil nil))
         (type (car types)))
      (cond ((type-case type :sequence)
             (mv nil t nil
                 (list (make-typed-variable :name (identifier "x")
                                            :type type))
                 nil nil))
            ((type-case type :set)
             (mv nil t nil
                 (list (make-typed-variable :name (identifier "x")
                                            :type type))
                 nil nil))
            (t (mv (list :builtin-wrong-type
                         (identifier-fix name)
                         (type-fix type))
                   nil nil nil nil nil)))))
   ((identifier-equiv name (identifier "add"))
    (b* (((unless (= (len types) 1))
          (mv (list :builtin-wrong-types
                    (identifier-fix name)
                    (type-list-fix types))
              nil nil nil nil nil))
         (type (car types)))
     (cond
      ((type-case type :sequence)
       (mv
        nil t
        (list
           (make-typed-variable :name (identifier "x")
                                :type (type-sequence->element type))
           (make-typed-variable :name (identifier "y")
                                :type type))
        (list (make-typed-variable :name (identifier "xy")
                                   :type type))
        nil nil))
      ((type-case type :set)
       (mv
          nil t
          (list (make-typed-variable :name (identifier "x")
                                     :type (type-set->element type))
                (make-typed-variable :name (identifier "y")
                                     :type type))
          (list (make-typed-variable :name (identifier "xy")
                                     :type type))
          nil nil))
      (t (mv (list :builtin-wrong-type
                   (identifier-fix name)
                   (type-fix type))
             nil nil nil nil nil)))))
   ((identifier-equiv name (identifier "append"))
    (b* (((unless (= (len types) 1))
          (mv (list :builtin-wrong-types
                    (identifier-fix name)
                    (type-list-fix types))
              nil nil nil nil nil))
         (type (car types)))
      (cond ((type-case type :sequence)
             (mv nil t
                 (list (make-typed-variable :name (identifier "x")
                                            :type type)
                       (make-typed-variable :name (identifier "y")
                                            :type type))
                 (list (make-typed-variable :name (identifier "xy")
                                            :type type))
                 nil nil))
            (t (mv (list :builtin-wrong-type
                         (identifier-fix name)
                         (type-fix type))
                   nil nil nil nil nil)))))
   ((identifier-equiv name (identifier "length"))
    (b* (((unless (= (len types) 1))
          (mv (list :builtin-wrong-types
                    (identifier-fix name)
                    (type-list-fix types))
              nil nil nil nil nil))
         (type (car types)))
      (cond ((type-case type :sequence)
             (mv nil t
                 (list (make-typed-variable :name (identifier "x")
                                            :type type))
                 (list (make-typed-variable :name (identifier "b")
                                            :type (type-integer)))
                 nil nil))
            ((type-case type :set)
             (mv nil t
                 (list (make-typed-variable :name (identifier "x")
                                            :type type))
                 (list (make-typed-variable :name (identifier "b")
                                            :type (type-integer)))
                 nil nil))
            (t (mv (list :builtin-wrong-type
                         (identifier-fix name)
                         (type-fix type))
                   nil nil nil nil nil)))))
   ((identifier-equiv name (identifier "is_empty"))
    (b* (((unless (= (len types) 1))
          (mv (list :builtin-wrong-types
                    (identifier-fix name)
                    (type-list-fix types))
              nil nil nil nil nil))
         (type (car types)))
      (cond ((type-case type :sequence)
             (mv nil t
                 (list (make-typed-variable :name (identifier "x")
                                            :type type))
                 (list (make-typed-variable :name (identifier "b")
                                            :type (type-boolean)))
                 nil nil))
            ((type-case type :set)
             (mv nil t
                 (list (make-typed-variable :name (identifier "x")
                                            :type type))
                 (list (make-typed-variable :name (identifier "b")
                                            :type (type-boolean)))
                 nil nil))
            (t (mv (list :builtin-wrong-type
                         (identifier-fix name)
                         (type-fix type))
                   nil nil nil nil nil)))))
   ((identifier-equiv name (identifier "first"))
    (b* (((unless (= (len types) 1))
          (mv (list :builtin-wrong-types
                    (identifier-fix name)
                    (type-list-fix types))
              nil nil nil nil nil))
         (type (car types)))
     (cond
      ((type-case type :sequence)
       (mv
        nil t
        (list (make-typed-variable :name (identifier "x")
                                   :type type))
        (list
          (make-typed-variable :name (identifier "y")
                               :type (type-sequence->element type)))
        (make-expression-unary
         :operator (unary-op-not)
         :operand
         (make-expression-call
          :function (identifier "is_empty")
          :types (list type)
          :arguments
          (list (make-expression-variable :name (identifier "x")))))
        nil))
      ((type-case type :set)
       (mv
        nil t
        (list (make-typed-variable :name (identifier "x")
                                   :type type))
        (list (make-typed-variable :name (identifier "y")
                                   :type (type-set->element type)))
        (make-expression-unary
         :operator (unary-op-not)
         :operand
         (make-expression-call
          :function (identifier "is_empty")
          :types (list type)
          :arguments
          (list (make-expression-variable :name (identifier "x")))))
        nil))
      (t (mv (list :builtin-wrong-type
                   (identifier-fix name)
                   (type-fix type))
             nil nil nil nil nil)))))
   ((identifier-equiv name (identifier "last"))
    (b* (((unless (= (len types) 1))
          (mv (list :builtin-wrong-types
                    (identifier-fix name)
                    (type-list-fix types))
              nil nil nil nil nil))
         (type (car types)))
     (cond
      ((type-case type :sequence)
       (mv
        nil t
        (list (make-typed-variable :name (identifier "x")
                                   :type type))
        (list
          (make-typed-variable :name (identifier "y")
                               :type (type-sequence->element type)))
        (make-expression-unary
         :operator (unary-op-not)
         :operand
         (make-expression-call
          :function (identifier "is_empty")
          :types (list type)
          :arguments
          (list (make-expression-variable :name (identifier "x")))))
        nil))
      (t (mv (list :builtin-wrong-type
                   (identifier-fix name)
                   (type-fix type))
             nil nil nil nil nil)))))
   ((identifier-equiv name (identifier "rest"))
    (b* (((unless (= (len types) 1))
          (mv (list :builtin-wrong-types
                    (identifier-fix name)
                    (type-list-fix types))
              nil nil nil nil nil))
         (type (car types)))
     (cond
      ((type-case type :sequence)
       (mv
        nil t
        (list (make-typed-variable :name (identifier "x")
                                   :type type))
        (list (make-typed-variable :name (identifier "y")
                                   :type type))
        (make-expression-unary
         :operator (unary-op-not)
         :operand
         (make-expression-call
          :function (identifier "is_empty")
          :types (list type)
          :arguments
          (list (make-expression-variable :name (identifier "x")))))
        nil))
      ((type-case type :set)
       (mv
        nil t
        (list (make-typed-variable :name (identifier "x")
                                   :type type))
        (list (make-typed-variable :name (identifier "y")
                                   :type type))
        (make-expression-unary
         :operator (unary-op-not)
         :operand
         (make-expression-call
          :function (identifier "is_empty")
          :types (list type)
          :arguments
          (list (make-expression-variable :name (identifier "x")))))
        nil))
      (t (mv (list :builtin-wrong-type
                   (identifier-fix name)
                   (type-fix type))
             nil nil nil nil nil)))))
   ((identifier-equiv name (identifier "member"))
    (b* (((unless (= (len types) 1))
          (mv (list :builtin-wrong-types
                    (identifier-fix name)
                    (type-list-fix types))
              nil nil nil nil nil))
         (type (car types)))
     (cond
      ((type-case type :sequence)
       (mv
        nil t
        (list
           (make-typed-variable :name (identifier "x")
                                :type (type-sequence->element type))
           (make-typed-variable :name (identifier "y")
                                :type type))
        (list (make-typed-variable :name (identifier "b")
                                   :type (type-boolean)))
        nil nil))
      ((type-case type :set)
       (mv
          nil t
          (list (make-typed-variable :name (identifier "x")
                                     :type (type-set->element type))
                (make-typed-variable :name (identifier "y")
                                     :type type))
          (list (make-typed-variable :name (identifier "b")
                                     :type (type-boolean)))
          nil nil))
      (t (mv (list :builtin-wrong-type
                   (identifier-fix name)
                   (type-fix type))
             nil nil nil nil nil)))))
   ((identifier-equiv name (identifier "remove_first"))
    (b* (((unless (= (len types) 1))
          (mv (list :builtin-wrong-types
                    (identifier-fix name)
                    (type-list-fix types))
              nil nil nil nil nil))
         (type (car types)))
     (cond
      ((type-case type :sequence)
       (mv
        nil t
        (list
           (make-typed-variable :name (identifier "x")
                                :type (type-sequence->element type))
           (make-typed-variable :name (identifier "y")
                                :type type))
        (list (make-typed-variable :name (identifier "z")
                                   :type type))
        nil nil))
      ((type-case type :set)
       (mv
          nil t
          (list (make-typed-variable :name (identifier "x")
                                     :type (type-set->element type))
                (make-typed-variable :name (identifier "y")
                                     :type type))
          (list (make-typed-variable :name (identifier "z")
                                     :type type))
          nil nil))
      (t (mv (list :builtin-wrong-type
                   (identifier-fix name)
                   (type-fix type))
             nil nil nil nil nil)))))
   (t (mv nil nil nil nil nil nil)))))

Theorem: booleanp-of-get-builtin-function-in/out/pre-post.foundp

(defthm booleanp-of-get-builtin-function-in/out/pre-post.foundp
  (b* (((mv ?err? ?foundp ?inputs
            ?outputs ?precondition? ?postcondition?)
        (get-builtin-function-in/out/pre-post name types)))
    (booleanp foundp))
  :rule-classes :rewrite)

Theorem: typed-variable-listp-of-get-builtin-function-in/out/pre-post.inputs

(defthm
 typed-variable-listp-of-get-builtin-function-in/out/pre-post.inputs
 (b* (((mv ?err? ?foundp ?inputs
           ?outputs ?precondition? ?postcondition?)
       (get-builtin-function-in/out/pre-post name types)))
   (typed-variable-listp inputs))
 :rule-classes :rewrite)

Theorem: typed-variable-listp-of-get-builtin-function-in/out/pre-post.outputs

(defthm
 typed-variable-listp-of-get-builtin-function-in/out/pre-post.outputs
 (b* (((mv ?err? ?foundp ?inputs
           ?outputs ?precondition? ?postcondition?)
       (get-builtin-function-in/out/pre-post name types)))
   (typed-variable-listp outputs))
 :rule-classes :rewrite)

Theorem: maybe-expressionp-of-get-builtin-function-in/out/pre-post.precondition?

(defthm
 maybe-expressionp-of-get-builtin-function-in/out/pre-post.precondition?
 (b* (((mv ?err? ?foundp ?inputs
           ?outputs ?precondition? ?postcondition?)
       (get-builtin-function-in/out/pre-post name types)))
   (maybe-expressionp precondition?))
 :rule-classes :rewrite)

Theorem: maybe-expressionp-of-get-builtin-function-in/out/pre-post.postcondition?

(defthm
 maybe-expressionp-of-get-builtin-function-in/out/pre-post.postcondition?
 (b* (((mv ?err? ?foundp ?inputs
           ?outputs ?precondition? ?postcondition?)
       (get-builtin-function-in/out/pre-post name types)))
   (maybe-expressionp postcondition?))
 :rule-classes :rewrite)

Theorem: get-builtin-function-in/out/pre-post-of-identifier-fix-name

(defthm get-builtin-function-in/out/pre-post-of-identifier-fix-name
  (equal (get-builtin-function-in/out/pre-post (identifier-fix name)
                                               types)
         (get-builtin-function-in/out/pre-post name types)))

Theorem: get-builtin-function-in/out/pre-post-identifier-equiv-congruence-on-name

(defthm
 get-builtin-function-in/out/pre-post-identifier-equiv-congruence-on-name
 (implies
    (identifier-equiv name name-equiv)
    (equal (get-builtin-function-in/out/pre-post name types)
           (get-builtin-function-in/out/pre-post name-equiv types)))
 :rule-classes :congruence)

Theorem: get-builtin-function-in/out/pre-post-of-type-list-fix-types

(defthm get-builtin-function-in/out/pre-post-of-type-list-fix-types
 (equal
   (get-builtin-function-in/out/pre-post name (type-list-fix types))
   (get-builtin-function-in/out/pre-post name types)))

Theorem: get-builtin-function-in/out/pre-post-type-list-equiv-congruence-on-types

(defthm
 get-builtin-function-in/out/pre-post-type-list-equiv-congruence-on-types
 (implies
    (type-list-equiv types types-equiv)
    (equal (get-builtin-function-in/out/pre-post name types)
           (get-builtin-function-in/out/pre-post name types-equiv)))
 :rule-classes :congruence)